Expand and combine like terms. $(3z^5+7z^2)^2=$
Answer: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ $\begin{aligned} &\phantom{=}\left(3z^5+7z^2\right)^2 \\\\ &=\left(3z^5\right)^2+2\left(3z^5\right)\left(7z^2\right)+\left(7z^2\right)^2 \\\\ &=9z^{10}+42z^7+49z^4 \end{aligned}$